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So this was one of the 6 questions in my last math assignment that challenged me a bit so I'm posting it here so that anyone who wants to brush up on solving PDE's or is just reeeally bored can have a go. I've already typed up my answer to this question and I'll post it in some hours time then see how it stacks up with any other answers posted (Want to check If I was on the right track)

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 May 28, 2015
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Here's what I thought the answer was:

 May 29, 2015

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